Question

ABC Corp. has a $3,000 par value bond outstanding with a coupon rate of 8 percent paid quarterly and 10 years to maturity. The yield to maturity of the bond is 4 percent.

a) What is the dollar price of the bond now?

b) If the bond dollar value drops to $3,000 after three years (t=3), what is the yield to maturity then? [Hint: explain in one sentence] - why is b 8% and how to work it out?

a) Par = 3000 C = 3,000 * 0.08 = 240 YTM-40% Face YTM/4(1YTM/4)10x4)(1 YTM/4)10x4 (1+1%)10x4) + 따 196)10x4 = 3985.04 1 % b) YTM is 8% because face value is equal to bond value.

Answer 1

(a) Face Value = $ 3000, Coupon Rate = 8 % paid quarterly, Tenure = 10 years or (4 x 10) = 40 quarters, Yield to Maturity = 4 % per annum or (4/4) = 1 % per quarter.

Quarterly Coupon = 0.08 x 3000 x 0.25 = $ 60

Bond Price = 60 x (1/0.01) x [1-{1/(1.01)^(40)}] + 3000 / (1.01)^(40) = $ 3985.04

(b) The coupon payment of a bond is equivalent to the bond's offered rate of return, whereas the yield to maturity is equivalent to its required rate of return. When the offered rate of return > required rate of return (such as in part(a)) the bond investor will have to pay a premium above face value to because of the extra return earned by holding the bond. On the other hand when the offered rate of return < required rate of return, the bond investor will buy the bond at a discount to face value as a compensation for accepting lower than required rate of return. In the case when both rates of return are equal, the bond investor will buy the bond at face value which is the case now. Hence, if the bond price falls to equal its face value, then the bond's yield to maturity will equal its annual coupon rate of 8%.